Reporting a Normality Test in SPSS
Wording the Check and the Decision
Reporting a normality test in SPSS is mostly a matter of placement and wording: a brief assumption check in the methods, naming what was examined, by which plots and tests, and what was decided. A significant p-value alone is not a verdict.
IN SHORT
Where an Assumption Check Belongs in a Report
An assumption check is reported briefly, usually in the analysis or methods section, and in the results only when it changed the analysis. The statement names what was examined, which for t-tests, ANOVA and regression means the residuals or the paired differences and not the raw outcome pooled across groups, the plots and tests used, and the decision taken. For reporting a normality test in SPSS, the evidence comes from Explore, with Normality plots with tests, under Analyze, Descriptive Statistics, and labels differ slightly between versions. Statements of this kind get a second reading at OnlineSPSS, a specialist statistical consultancy for academic, clinical and professional research, where an in-house PhD-level statistician works from the model output.
In This Guide
METHOD SUPPORT
The Analyses Whose Assumptions Are Checked
The check belongs to a larger analysis, and the two pages below cover the method families in which it most often appears.
Comparative & Hypothesis Testing
Group comparisons for continuous and ordinal outcomes, planned for your design with the distributional question settled in advance.
Multiple Linear Regression
A model whose residual diagnostics and influential cases are reported with the coefficients and their confidence intervals.
BEFORE THE SENTENCE
Design Features the Statement Depends On
These facts come from the design and the diagnostics, and each one changes what is checked and what the report can say.
What Was Examined Name the quantity: residuals from the fitted model, differences between paired scores, or the outcome within each group. The pooled outcome rarely answers the assumption.
Sample Size A test is read with n. Small samples give little power to detect departures, and very large ones flag trivial departures, so the plots carry the weight in both.
Planned or Reactive Say whether the check and the response to it were set in the analysis plan. A response chosen after seeing the results is described as such, with the reason for it.
Consequence of a Departure State what a departure would change. Inference on means is often fairly tolerant of it at moderate group sizes, while prediction intervals and very small samples are not.
IN SPSS
Taking the Evidence From the Output
IBM SPSS prints the evidence from Explore, and what each test can and cannot establish is covered in Normality Tests in SPSS and What They Mean.
Save the Residuals or Differences
For a model fitted in Linear Regression or GLM Univariate, save the residuals through Save. For a paired design, compute the difference score. These are the variables examined.
Check: Saved residuals appear as new variables in the Data View, and the unstandardized and standardized versions differ in scale. The statement names which kind was examined.
Take the Q-Q Plot and Histogram
Request Normality plots with tests in Explore, and take the Normal Q-Q Plot and the histogram for each variable examined.
Tip: Describe what the plot showed in a few words, such as a slight right skew or heavy tails. A reviewer can then judge the departure, which a p-value does not describe.
Take the Shapiro-Wilk Row
From the Tests of Normality table, take the Shapiro-Wilk Statistic, df and Sig., ignoring the Kolmogorov-Smirnov row unless a reason is given for it.
Watch: In this table df equals the number of cases in the tested group, so it is the n of that group and not a degrees-of-freedom term from a model.
Take Skewness and Kurtosis
If they are cited, take Skewness and Kurtosis with their standard errors from the Descriptives table of Explore.
Check: The ratio of a statistic to its standard error rises with n, so in large samples it flags departures too small to matter. Quote the values and judge their size.
Record the Decision Taken
Note down what followed from the check: the planned analysis kept, a transformation, a robust or resampling method, or a different model.
Tip: File the plot or table that drove the decision with the analysis files, so the supplementary table can cite it and anyone can retrace the choice later.
Place the Statement in the Methods
Set out the check in one or two sentences for the methods or analysis section, with the detail in a supplementary table or a note.
Check: Compare the sentence with the output for the same variables, groups and n, and give W and p with the decimals printed, with p below .001 shown as such.
READING THE OUTPUT
Where Each Normality Output Value Goes in the Report
Normality evidence is printed across Tests of Normality, Descriptives and the charts, and each part has a different place in a manuscript.
| Output value | Where SPSS prints it | Where it goes and what to check |
|---|---|---|
| Shapiro-Wilk, Statistic and Sig. | Tests of Normality table | W with its p in the clause or the supplement, read with the plot and the size of the group |
| df in the Shapiro-Wilk row | Tests of Normality table | The n of the group; some authors place it in parentheses after W |
| Kolmogorov-Smirnov with Lilliefors Significance Correction | Tests of Normality table | Usually left out when Shapiro-Wilk is given, unless the journal or field asks for it |
| Skewness and Kurtosis, with Std. Error | Descriptives table of Explore | Optional support; the values and their size are given, not only a ratio |
| Normal Q-Q Plot | Charts in the Explore output | The main evidence, described in words and shown in the supplement |
| Detrended Normal Q-Q Plot | Charts in the Explore output | Departures from the line made easier to see, if a plot is shown |
| Histogram | Charts in the Explore output, if requested | The shape of the distribution, with any skew or outlier mentioned |
| Extreme Values | Explore output | Outliers that may drive a departure, handled and reported as a separate decision |
| Standardized residuals saved from the model | New variable in the Data View | The variable examined for t-tests, ANOVA and regression models |
REPORTING
A Methods Sentence and a Short Assumption Table
The sentence goes in the methods, the table can sit in a supplement, and both name the same quantity, plot, test and decision.
Reporting assumption checks in a methods section takes one or two sentences, and reporting a Shapiro-Wilk test in APA style needs only a short clause, W = ___, p = ___, tied to the plot that supports it. The frame below suits a model fitted to several groups, and a paired design replaces the residuals with the differences. The check is reported as a decision with its reason, so a reader sees what was done and why, and not as a pass or fail. If the response was a robust method, a transformation or a different model, the sentence names it. The detail of each check belongs in a supplementary table or a note.
Normality of the [residuals / paired differences / outcome within each group] was assessed with normal Q-Q plots and the Shapiro-Wilk test. The plots showed [no marked departure / a slight right skew / heavy tails], and the Shapiro-Wilk statistic was W = ___, p = ___ (n = ___). Given [the size of the departure and the group sizes], the planned [analysis] was [retained / replaced by ___], [as specified in the analysis plan / as decided after inspecting the data].
| Table S1. Assumption Checks for the Analyses in [Section] | |||
|---|---|---|---|
| Analysis | Quantity examined and plot | W (p), n | Decision |
| [Analysis 1] | [Residuals]; Q-Q plot: [description] | ___ (___), n = ___ | [Retained / alternative] |
| [Analysis 2] | [Differences]; Q-Q plot: [description] | ___ (___), n = ___ | [Retained / alternative] |
| [Analysis 3] | [Residuals]; Q-Q plot: [description] | ___ (___), n = ___ | [Retained / alternative] |
| Note. W = Shapiro-Wilk statistic. Decisions rest on the size and shape of the departures and on group sizes, not on the p-value alone. | |||
An assumption check has no effect size, so the departure is described in terms a reader can judge: its direction and shape from the plot, skewness and kurtosis with their sizes, and the part of the distribution where points leave the line. In a large sample a significant Shapiro-Wilk result is expected for trivial departures and is not reported as a reason to change the test. In a small sample a nonsignificant result is weak evidence of normality, because power is low. Both situations are handled by describing the departure and its likely effect on the planned inference.
COMMON MISTAKES
Statements That Misstate the Evidence
Each of these shows when the sentence is held against the plots and the table it was drawn from.
Cases Removed Until the Test Passes Dropping extreme cases until Shapiro-Wilk stops being significant fits the data to the check. Each exclusion is reported with its rule and the number of cases removed, and the results with and without them are shown side by side.
A Test Offered as the Only Evidence A p-value says nothing about the size or shape of a departure. A statement resting on it alone, without the Q-Q plot, cannot be evaluated by the reader at all.
One Sentence for Several Analyses One line claiming that normality held throughout hides which residuals or differences were examined for which analysis. Each analysis gets its own clause, or the supplementary table lists them all.
Kolmogorov-Smirnov Without Its Correction Quoting the Kolmogorov-Smirnov row without saying that SPSS applies the Lilliefors correction leaves readers to assume the classic test, whose p-values differ. Where that row is reported, the correction is named.
The Decision Left Out Saying only that normality was checked leaves the reader unsure what followed. The sentence says what was kept, transformed or replaced, with the reason.
Data-Driven Choices Presented as Planned A response chosen after the data were inspected is described as such. Presenting it as planned misrepresents the analysis, and the methods text is where this is noticed.
Checked the raw scores instead of the residuals? Independent Statistical Review examines whether the check and the decision fit the model that was run.
FREQUENTLY ASKED QUESTIONS
Authors' Doubts When Reporting a Normality Test in SPSS
The sentence sits in different parts of a manuscript, changes after a transformation and must not claim more than a nonsignificant result can show.
Should the normality test appear in the main text?
Usually briefly in the methods or analysis section, with the detail in a supplement. It moves to the results only when the check changed the analysis. Journal instructions and the convention of the field decide the rest, and the sentence names the quantity examined, the plot and the decision taken.
How is a transformation reported in the results?
Name the transformation and its reason, then say whether estimates are shown on the analyzed scale or back-transformed. After a log transformation, a back-transformed difference between means is a ratio of geometric means, and the wording says that. An analysis on the original scale, if also run, can sit in a supplement for comparison.
Is a nonsignificant Shapiro-Wilk result proof of normality?
No, because the test has low power in small samples and a nonsignificant result cannot confirm the null hypothesis. The sentence says that no marked departure was seen in the plots and the test did not indicate one, and it avoids saying that normality was established or verified.
Who reviews an assumption-check statement before submission?
Reading starts from the plots and tables of the model that was run. An in-house PhD-level statistician at OnlineSPSS confirms the quantity examined and the decision recorded, then proposes plainer wording where a sentence claims too much. This falls under Results Reporting & Interpretation, and which analysis to run stays the researcher’s choice.
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NEXT STEP
Does the Check Match
the Model You Ran?
An assumption statement is tied to a model, to the residuals or differences examined and to a decision. In a sentence you already have, the quantity it names is the first thing compared with the plots.
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